RED PARABOLA: y=x^{2} (Quadratic parent function)

GREEN PARABOLA: y=1/8x^{2}+2 (Opens up and is wider)

BLUE PARABOLA: y=-6x^{2}-2 (Opens down and is narrower)

ORANGE PARABOLA: y=(x-5)^{2}+1 (Shifted right)

PURPLE PARABOLA: y=x^{2}-5 (Shifted down)

PARAGRAPH

In my equations, a, h, and k are significant because they allow the movement of the parabolas to meet the necessary criteria. The red parabola is the parent function which all the other parabolas are based off of. With the green parabola I changed the a value to be 1/8 to make the parabola open upwards and wider than the original parabola. I also made the h value equal positive 2 to make the y value of the vertex 2 moving the parabola up on the graph. With the blue parabola I made the a value equal to –6 causing the parabola to open downwards and become narrower than the parent function. I made the h value equal to –2 leading to the y value of the vertex equaling –2 moving the parabola down the graph. With the orange parabola I made the h value equal to 5 resulting in the parabola being shifted to the right. I also made the k value equal to 1 causing the parabola to be shifted up. Finally, with the purple parabola I made the k value equal to –5 resulting in the parabola being shifted downwards.  

SELF-ASSESSMENT

1. How did you represent the same mathematical idea in multiple ways in this assignment?

I represented the same mathematical idea in multiple ways in this assignment by using different values to change the shape and where the parabolas are placed on the graph. The mathematical idea is transforming parabolas and I did that in multiple ways by creating different parabolas to fit the criteria. So, the idea of transforming parabolas was represented by different values changing the shape and location of parabolas on the graph.

2. State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.

Vertex: the highest/lowest point on the parabola.

h value: the value that shifts the parabola horizontally.

k value: the value that shifts the parabola vertically.

a value: value that determines if that parabola opens upwards, or downwards and if the parabola will be wide or narrow.

Parent Function: the simplest version of a parabola.

3. How did you use formatting to share your information in a clear and organized way?

I used formatting to share my information in a clear and organized way in this assignment by not making the first three parabolas have the same vertex. I moved two of them either up or down to make the graph look less cramped. I also used formatting to make the graph the perfect size so all the lines are visible but not too big the lines are too small.